Network Reliability: The effect of local network structure on diffusive processes

TL;DR

This study revisits the network reliability polynomial to analyze how local network structures like assortativity and triangles influence the spread of diseases, using simulations on various random graph models.

Contribution

It introduces a new representation of the network reliability polynomial suitable for distributed estimation and explores the effects of local structures on network reliability.

Findings

Positively or neutrally assortative graphs are more reliable.

Increasing triangles does not necessarily increase reliability.

Assortativity-by-degree significantly impacts network robustness.

Abstract

This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is well-suited for estimation by distributed simulation. We describe a collection of graphs derived from Erd\H{o}s-R\'enyi and scale-free-like random graphs in which we have manipulated assortativity-by-degree and the number of triangles. We evaluate the network reliability for all these graphs under a reliability rule that is related to the expected size of a connected component. Through these extensive simulations, we show that for positively or neutrally assortative graphs, swapping edges to increase the number of triangles does not increase the network reliability. Also, positively assortative graphs are more reliable than neutral or disassortative graphs with the same number of edges. Moreover, we show the combined effect of both assortativity-by-degree and the presence of triangles on the critical point and the size of the smallest subgraph that is reliable.